Calculating Anand's Original Item Cost

This explanation focuses on finding the initial purchase price of an item bought by Anand. We will work backward from the final sale price, considering the profit Anand made and the loss Bharath incurred, along with Anand's repair expenses.

Step 1: Finding Bharath's Purchase Price

Bharath sold the item for ₹4,480, which represented a 44% loss on his purchase price. This means that ₹4,480 is equal to 100% - 44% = 56% of what Bharath paid for it.

Let $C_B$ be the cost price for Bharath.

The relationship can be written as:

$₹4,480 = C_B \times (100\% - 44\%)$

$₹4,480 = C_B \times 56\%$

$₹4,480 = C_B \times 0.56$

To find $C_B$, we calculate:

$C_B = \frac{₹4,480}{0.56}$

$C_B = ₹8,000$

So, Bharath's cost price was ₹8,000.

Step 2: Determining Anand's Selling Price

The price Bharath paid for the item is the same price Anand sold it for. Therefore, Anand's selling price ($S_A$) was ₹8,000.

$S_A = ₹8,000$

Step 3: Calculating Anand's Total Cost

Anand sold the item at a 25% profit. This profit was calculated based on Anand's total cost, which included the original purchase price plus the ₹169 spent on repairs. Anand's selling price ($S_A$) is therefore 100% + 25% = 125% of his total cost ($C_{A, \text{total}}$).

We can express this as:

$S_A = C_{A, \text{total}} \times (100\% + 25\%)$

₹8,000 = $C_{A, \text{total}} \times 125\%$

₹8,000 = $C_{A, \text{total}} \times 1.25$

To find Anand's total cost, we calculate:

$C_{A, \text{total}} = \frac{₹8,000}{1.25}$

$C_{A, \text{total}} = ₹6,400$

Anand's total cost, including repairs, amounted to ₹6,400.

Step 4: Finding Anand's Original Purchase Price

Anand's total cost ($C_{A, \text{total}}$) includes his original purchase price ($C_{A, \text{original}}$) and the repair expenses.

$C_{A, \text{total}} = C_{A, \text{original}} + \text{Repair Expenses}$

₹6,400 = $C_{A, \text{original}} + ₹169$

To find the original purchase price, we subtract the repair costs:

$C_{A, \text{original}} = ₹6,400 - ₹169$

$C_{A, \text{original}} = ₹6,231$

Thus, the original cost of the item for Anand was ₹6,231.